Subgroups — Dic₅×#803 #14294218

Order 1920.

720 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#91087	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄²×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×#90952	C₂	1	2	yes	maximal
5	C₂×Dic₅×C₃⋊C₈	C₂	1	2	yes	maximal
6	Dic₅×#97	—	3	1	no	maximal, Hall
7	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃⋊#168	C₂²	1	2	yes	—
9	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
10	C₂×C₃×C₄×Dic₅	C₄	1	4	yes	—
11	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
13	#91087	C₄	1	4	yes	complemented
14	C₅×#803	C₄	1	4	yes	complemented
15	#90952	C₄	1	8	yes	complemented
16	Dic₅×C₃⋊C₈	C₄	1	8	yes	complemented
17	C₄×#803	—	5	1	no	maximal, Hall
18	C₂×C₅×#97	—	3	1	no	—
19	C₂×#3947	—	3	2	no	—
20	C₂×C₈×Dic₅	—	3	2	no	—
21	C₄²×Dic₅	D₃	1	1	yes	characteristic
22	C₂×#3935	—	3	1	no	—
23	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
24	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
25	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
26	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
27	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
28	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
29	C₂×C₃⋊#168	C₂×C₄	1	4	yes	—
30	C₂×C₃⋊#168	C₂×C₄	1	4	yes	—
31	C₂×C₃⋊#168	C₂×C₄	1	4	yes	—
32	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
33	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
34	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	—
35	C₃×C₄×Dic₅	—	2	8	no	—
36	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
37	C₃×C₄×Dic₅	C₂×C₄	1	4	yes	—
38	C₃×C₄³	—	5	1	no	—
39	C₂×#803	—	5	1	no	—
40	C₂×#803	—	5	2	no	—
41	C₂×#803	D₅	1	1	yes	characteristic
42	C₂×C₄×C₃⋊C₈	—	5	2	no	—
43	C₂²×C₅×C₈	—	3	2	no	—
44	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
45	C₂×C₄×Dic₅	Dic₃	1	4	yes	—
46	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
47	C₂×C₄×Dic₅	C₂×D₃	1	1	yes	characteristic
48	C₂²×#168	—	3	2	no	—
49	C₅×#97	—	3	4	no	—
50	#3947	—	3	8	no	—
51	C₈×Dic₅	—	3	8	no	—
52	#3935	—	3	4	no	—
53	C₄×#97	—	15	1	no	Sylow
54	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₃×C₄×C₅	—	2	4	no	—
56	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
57	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
58	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
59	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₃×Dic₅	—	2	4	no	—
62	C₂×C₃×Dic₅	C₄²	1	4	yes	—
63	C₂×C₃×Dic₅	C₄²	1	4	yes	—
64	C₂×C₃×Dic₅	M₁₆	1	8	yes	—
65	C₃⋊#168	C₄²	1	8	yes	complemented
66	C₅×C₃⋊C₈	C₄²	1	8	yes	complemented
67	C₂×C₃×C₄²	—	5	1	no	—
68	C₂×C₃×C₄²	—	5	1	no	—
69	C₂×C₃×C₄²	—	5	4	no	—
70	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
71	C₂²×C₃⋊C₈	—	5	2	no	—
72	C₂²×C₃⋊C₈	C₂×D₅	1	2	yes	—
73	#803	—	5	4	no	—
74	#803	—	5	8	no	—
75	#803	Dic₅	1	4	yes	direct product factor
76	C₄×C₃⋊C₈	—	5	8	no	—
77	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
78	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
79	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
80	C₂²×Dic₅	C₂×Dic₃	1	2	yes	—
81	C₂×C₅×C₈	—	3	4	no	—
82	C₂×C₅×C₈	—	3	4	no	—
83	C₂×C₅×C₈	—	3	4	no	—
84	C₄²×C₅	C₄×D₃	1	2	yes	—
85	C₄²×C₅	C₄×D₃	1	2	yes	—
86	C₄×Dic₅	—	2	8	no	—
87	C₄×Dic₅	C₄×D₃	1	4	yes	—
88	C₄×Dic₅	C₄×D₃	1	4	yes	—
89	C₂×#168	—	3	4	no	—
90	C₂×#168	—	3	4	no	—
91	C₂×#168	—	3	4	no	—
92	C₂×#97	—	3	1	no	—
93	C₂×#97	—	15	2	no	—
94	C₂×#97	—	15	1	no	—
95	C₂×C₄×C₈	—	15	2	no	—
96	C₄³	—	5	1	no	—
97	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
98	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
99	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
100	C₂²×C₃×C₅	C₂×M₁₆	1	4	yes	—
101	C₃×C₄×C₅	—	2	4	no	—
102	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
103	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
104	C₃×Dic₅	—	2	4	no	—
105	C₃×Dic₅	#97	1	8	yes	complemented
106	C₂²×C₃×C₄	—	5	2	no	—
107	C₂²×C₃×C₄	—	5	2	no	—
108	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
109	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
110	C₃×C₄²	—	5	4	no	—
111	C₃×C₄²	—	5	4	no	—
112	C₃×C₄²	—	10	8	no	—
113	C₃×C₄²	C₄×D₅	1	2	yes	—
114	C₃×C₄²	C₂×Dic₅	1	2	yes	—
115	C₂×C₃⋊C₈	—	5	4	no	—
116	C₂×C₃⋊C₈	—	5	4	no	—
117	C₂×C₃⋊C₈	—	5	4	no	—
118	C₂×C₃⋊C₈	C₄×D₅	1	4	yes	—
119	C₂×C₃⋊C₈	C₄×D₅	1	4	yes	—
120	C₂×C₃⋊C₈	C₂×Dic₅	1	4	yes	—
121	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
122	C₂×C₄×C₅	—	2	4	no	—
123	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
124	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
125	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
126	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
127	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
128	C₂×Dic₅	—	2	4	no	—
129	C₂×Dic₅	#208	1	8	yes	—
130	C₂×Dic₅	C₄×Dic₃	1	4	yes	—
131	C₂×Dic₅	C₄×Dic₃	1	4	yes	—
132	C₅×C₈	—	3	8	no	—
133	#168	—	3	8	no	—
134	C₂²×C₈	—	3	2	no	—
135	C₂²×C₈	—	15	2	no	—
136	C₂×C₄²	—	5	1	no	—
137	C₂×C₄²	—	5	1	no	—
138	C₂×C₄²	—	5	4	no	—
139	C₂×C₄²	D₃×D₅	1	1	yes	characteristic
140	#97	—	3	4	no	—
141	#97	—	15	8	no	—
142	#97	—	15	4	no	—
143	C₄×C₈	—	15	8	no	—
144	C₂×C₃×C₅	C₄³	1	1	yes	characteristic
145	C₂×C₃×C₅	C₂×#97	1	2	yes	—
146	C₂×C₃×C₅	C₄×M₁₆	1	2	yes	—
147	C₂×C₃×C₅	C₄×M₁₆	1	2	yes	—
148	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
149	C₂×C₃×C₄	—	2	4	no	—
150	C₂×C₃×C₄	—	5	4	no	—
151	C₂×C₃×C₄	—	5	8	no	—
152	C₂×C₃×C₄	—	5	4	no	—
153	C₂×C₃×C₄	—	10	4	no	—
154	C₂×C₃×C₄	C₄×Dic₅	1	4	yes	—
155	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
156	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
157	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
158	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
159	C₃⋊C₈	—	5	8	no	—
160	C₃⋊C₈	C₄×Dic₅	1	8	yes	complemented
161	C₂²×C₅	C₂×#208	1	4	yes	—
162	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
163	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
164	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
165	C₄×C₅	—	2	4	no	—
166	C₄×C₅	C₄²×D₃	1	2	yes	—
167	C₄×C₅	C₄²×D₃	1	2	yes	—
168	Dic₅	—	2	4	no	—
169	Dic₅	#803	1	8	yes	direct product factor
170	C₂²×C₄	—	5	2	no	—
171	C₂²×C₄	—	5	2	no	—
172	C₂²×C₄	D₅×Dic₃	1	2	yes	—
173	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
174	C₂×C₈	—	3	4	no	—
175	C₂×C₈	—	3	4	no	—
176	C₂×C₈	—	3	4	no	—
177	C₂×C₈	—	15	4	no	—
178	C₂×C₈	—	15	4	no	—
179	C₂×C₈	—	15	4	no	—
180	C₄²	—	5	4	no	—
181	C₄²	—	5	4	no	—
182	C₄²	—	10	8	no	—
183	C₄²	D₃×Dic₅	1	2	yes	—
184	C₄²	#1200	1	2	yes	—
185	C₃×C₅	C₄×#97	1	1	yes	characteristic, complemented, Hall
186	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
187	C₂²×C₃	C₄²×D₅	1	1	yes	characteristic
188	C₂²×C₃	D₅×M₁₆	1	4	yes	—
189	C₂²×C₃	C₂×C₄×Dic₅	1	1	yes	characteristic
190	C₃×C₄	—	2	4	no	—
191	C₃×C₄	—	5	8	no	—
192	C₃×C₄	—	10	4	no	—
193	C₃×C₄	C₄²×D₅	1	2	yes	—
194	C₃×C₄	C₂×C₄×Dic₅	1	2	yes	—
195	C₂×C₅	C₂×#803	1	2	yes	—
196	C₂×C₅	C₄×#208	1	2	yes	—
197	C₂×C₅	C₄×#208	1	2	yes	—
198	C₂×C₅	C₄²×Dic₃	1	1	yes	characteristic
199	C₂³	C₂×D₅×Dic₃	1	1	yes	characteristic
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	5	8	no	—
202	C₂×C₄	—	5	4	no	—
203	C₂×C₄	—	5	4	no	—
204	C₂×C₄	—	10	4	no	—
205	C₂×C₄	Dic₃×Dic₅	1	4	yes	—
206	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
207	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
208	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
209	C₂×C₄	C₂×#1200	1	1	yes	characteristic
210	C₈	—	3	8	no	—
211	C₈	—	15	8	no	—
212	C₂×C₃	D₅×#97	1	2	yes	—
213	C₂×C₃	#64996	1	2	yes	—
214	C₂×C₃	C₄²×Dic₅	1	1	yes	characteristic
215	C₂×C₃	M₁₆×Dic₅	1	2	yes	—
216	C₅	C₄×#803	1	1	yes	characteristic, complemented, Sylow
217	C₂²	D₅×#208	1	4	yes	—
218	C₂²	C₄×D₅×Dic₃	1	1	yes	characteristic
219	C₂²	C₄×D₅×Dic₃	1	1	yes	characteristic
220	C₂²	C₂×Dic₃×Dic₅	1	1	yes	characteristic
221	C₄	—	2	4	no	—
222	C₄	—	5	8	no	—
223	C₄	—	10	4	no	—
224	C₄	C₄×D₃×Dic₅	1	2	yes	—
225	C₄	C₄×#1200	1	2	yes	—
226	C₃	Dic₅×#97	1	1	yes	characteristic, complemented, Sylow
227	C₂	D₅×#803	1	2	yes	—
228	C₂	#11747003	1	2	yes	—
229	C₂	Dic₅×#208	1	2	yes	—
230	C₂	C₄×Dic₃×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂×D₃×D₅
commutator	C₂×C₃×C₅	C₄³
Fitting	C₂×C₃×C₄²×C₅	C₂²
socle, prime radical	C₂³×C₃×C₅	C₂²×C₄
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂×C₄²	D₃×D₅
hypocenter	C₃×C₅	C₄×#97
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
13. #91087	C₄	semidirect
14. C₅×#803	C₄	semidirect
15. #90952	C₄	semidirect
16. Dic₅×C₃⋊C₈	C₄	semidirect
65. C₃⋊#168	C₄²	semidirect
66. C₅×C₃⋊C₈	C₄²	semidirect
75. #803	Dic₅	direct (N × H)
105. C₃×Dic₅	#97	semidirect
160. C₃⋊C₈	C₄×Dic₅	semidirect
169. Dic₅	#803	direct (N × H)
185. C₃×C₅	C₄×#97	semidirect
216. C₅	C₄×#803	semidirect
226. C₃	Dic₅×#97	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#91087	2
C₂×C₅×#803	2
C₃×C₄²×Dic₅	2
C₂×#90952	2
C₂×Dic₅×C₃⋊C₈	2
Dic₅×#97	3
C₄×#803	5

Subgroups — Dic5×#803 #14294218

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₅×#803 #14294218